I have been reading a book on Macoy rings and I saw these definitions for the annihilator sets: let $R$ be a ring and $I$ an ideal of $R$. $$(I:a)=\{r\in R: ra\in I\}~~\text{and}~~(0:a)=\{r\in R: ra=0\}.$$ My question is, do we have rings for which $$(I:a)=(0:a)$$ or for which $$(I:a)\cong(0:a)?$$
2026-04-01 10:23:59.1775039039
Do we have rings for which $(I:a)=(0:a)$ or for which $(I:a)\cong(0:a)?$
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